Numerical Study of TAP Metastable States in 3-body Ising Spin Glasses

The distribution of solutions of the Thouless-Anderson-Palmer equation is studied by extensive numerical experiments for fully connected 3-body interaction Ising spin glass models in a level of annealed calculation. A recent study predicted that when the equilibrium state of the system is characterized by one-step replica symmetry breaking, the distribution is described by a Becchi-Rouet-Stora-Tyutin (BRST) supersymmetric solution in the relatively low free energy region, whereas the BRST supersymmetry is broken for higher values of free energy (Crisanti et al., Phys. Rev. B 71 (2005) 094202). Our experiments qualitatively reproduce the discriminative behavior of macroscopic variables predicted by the theoretical assessment.Comment: 13 pages, 4 figure

Sequential Minimization of the Bethe Free Energy of Ising Spin Systems

A technique for minimizing the Bethe free energy of Ising spin systems is presented. The technique is based on a property of the Bethe free energy that diagonal elements of the Hessian are generally positive. This implies that solving the extremum condition with respect to a single element with fixing others at each update yields a unique solution which can be easily found by efficient algorithms such as a bisection method and reduces the value of the Bethe free energy. The proposed method, therefore, iterates sequential minimization with respect to a single element, which probably leads to convergence to a local minimum. Practical relevance of the scheme is shown by an application to a problem of multidimensional probabilistic reasoning that arises in a modern wireless communication system